desp: Robust estimation of a sparse precision matrix

Description

This function computes robust estimates of the precision matrix $Omega$ and of the expectation $mu$ corresponding to the data matrix X by solving a convex optimization problem. It implements the algorithms proposed by Balmand and Dalalyan (2015a, 2015b).

Usage

desp(X,lambda=0,gamma=0,settings=NULL)

Arguments

The data matrix.

lambda

The penalization parameter that encourages robustness.

gamma

The penalization parameter that promotes sparsity.

settings

A list including all the parameters needed for the estimation.

Value

desp returns an object with S3 class "desp" containing the estimated parameters, with components:

References

Balmand, S. and Dalalyan, A. S. (2015a): On estimation of the diagonal elements of a sparse precision matrix, Posted as http://arxiv.org/abs/1504.04696.

Balmand, S. and Dalalyan, A. S. (2015b): Convex programming approach to robust estimation of a multivariate Gaussian model, Posted as http://arxiv.org/abs/1512.04734.

Examples

Run this code

## set the dimension and the sample size
p <- 50
n <- 40
## define the true precision matrix
Omega <- 2*diag(p)
Omega[1,1] <- p 
Omega[1,2:p] <- 2/sqrt(2)
Omega[2:p,1] <- 2/sqrt(2)
## generate the distribution
set.seed(1)
X <- MASS::mvrnorm(n, rep.int(0,p), MASS::ginv(Omega))
## define the settings
settings <- list("diagElem"="AD", "OLS"=FALSE)
## estimate the parameters of the distribution
params <- desp(X,lambda=0,gamma=sqrt(2*log(p)),settings=settings)
## error of estimation measured by Frobenius norm
sqrt(sum((Omega - params$Omega)^2))
## increase the sample size and generate the distribution again
n <- 1000
X <- MASS::mvrnorm(n, rep.int(0,p), MASS::ginv(Omega))
## estimate the parameters of the distribution
params <- desp(X,lambda=0,gamma=sqrt(2*log(p)),settings=settings)
## error of estimation measured by Frobenius norm
sqrt(sum((Omega - params$Omega)^2))